关于两类具有不同基函数的标准模糊系统逼近精度问题的研究

在标准模糊系统的基础上提出了以正规二次多项式和正规三角函数为基函数的两类标准模糊系统.通过采用数值分析中的余项与辅助函数方法,对这两类模糊系统进行了误差精度的分析,给出了从SISO到MISO的误差界公式.同时,对这两类模糊系统误差界进行了比较,指出了两类模糊系统的优劣.最后,通过算例验证了理论结果的正确性.     

两类特殊的联系函数(Copula)

提出两类联系函数,它们是阿基米德联系函数与F réchet-Hoeffd ing界的融合,是正序簇.一类介于F réchet-Hoeffd ing下界与一个特殊的联系函数之间;另一类介于F réchet-Hoeffd ingshang上界与一个特殊的联系函数之间.本文最后提出几个有待解决的问题.     

奇可标号图类最优界定函数的相关研究

令G表示一类图.如果存在一个函数f使得对于任意的G∈G都有χ(G)≤f(ω(G)),那么称G是χ-界图类,且称f是G的一个界定(binding)函数.本文研究奇可标号图类最优界定函数相关问题,证明一类无4-洞奇可标号图有线性界定函数.     

广义变分不等式的广义间隙函数和误差界

针对两类广义变分不等式,分别定义了几族广义间隙函数,并研究其性质.利用这些广义间隙函数,在所研究变分不等式问题的目标函数F关于解是g-强单调的条件下,得到了误差界估计,这里不需要假设F是连续可微或局部Lipschitz的.     

基于 HNBUE(HNWUE) 寿命分布类的M/G/1排队等待时间分布函数的指数型界值

本文考虑一个M/G/1排队,其中顾客到达率为λ(0)和服务时间分布函数为G(t).在顾客服务时间的分布函数G(t)具有HNBUE(HNWUE)分布类特性的条件下,本文研究等待时间分布函数的界值问题,得到等待时间分布函数的易于计算的、有实用价值的指数型界值表达式,并通过计算例子表明所得结果有应用价值.     

关于一类奇异积分算子的加权不等式

其中上确界对所有的方体Qx而取。 本文中提到的方体Q总是边平行于坐标轴的。记M=M_1,即Hardy-Littlewood极大算子。 A_p(1≤p≤∞)函数类就是通常所说的满足B.Muckenhoupt的A_p-条件的函数类(可见[1])。     

各向异性Besov-Wiener类由多重样本的最优恢复

研究各向异性Besov-Wiener类SrpqθB（R^n）在Lq（R^n）,（1＜q≤P＜∞）中由其函数和它们的导数样本的最优恢复问题,确定了误差界的精确阶.     

三角函数的推广

利用函数方程定义仿正切函数类,再用仿正切函数定义仿正、余弦函数类,并对这些函数类进行研究.所定义的函数类中的函数具有通常三角函数的性质及运算规律,故而可将其作为三角函数的某种推广.通过实例证实.了通常的正切函数其实是仿正切函数的一种解析延拓.     

连续函数用它的富里埃级数的线性平均数的逼近问题

<正> 在函数的逼近理论中,相当重要的分支是研究连续周期函数用它的富里埃级数的各种平均数来逼近的问题.对于重要的平均数,如典型平均数、瓦来一布然平均数、蔡查罗平均数等等,在相当广泛的函数类中,利用这些平均数来逼近函数的逼近度的上确界,都已经有了渐近表达式.假设 f(x)是以2π为周期的函数以下简记 f(x)∈C_(2π),     

G -函数与迭代阵谱半径的估计

该文应用G -函数概念, 获得了迭代矩阵谱半径新的上、下界, 所得结果推广和改进了文献[1--6]中的相应结果.这些结果适合于更广泛的矩阵类, 数值结果也表明在相同的条件下这些新界优于文献[1--6]中的界.     

Minimax theorems and cone saddle points of uniformly same-order vector-valued functions

This paper is concerned with minimax theorems in vectorvalued optimization. A class of vector-valued functions which includes separated functionsf(x, y)=u(x)+v(y) as its proper subset is introduced. Minimax theorems and cone saddle-point theorems for this class of functions are investigated.The authors would like to thank two anonymous referees for helpful comments.     

Semi-B-Preinvex Functions

In this note, a class of functions, called semi-B-preinvex function, which are a generalization of the semipreinvex functions and the B-vex functions, is introduced. Examples are given to show that there exist functions which are semi-B-preinvex functions, but are neither semipreinvex nor B-vex. A property of the semi-B-preinvex functions is obtained.Communicated by F. GiannessiThis research was partially supported by a Science Committee Project, Research Foundation of Chongqing, Grant 8409. The authors are thankful to the referees and Prof. F. Giannessi for suggestions and comments which helped to give the present form to this paper.     

Tangentially continuous directional derivatives in nonsmooth analysis

In this paper, we introduce a new class of nonsmooth functions in terms of a continuity property of the usual directional derivative. Under this approach, we study the subregular and the semismooth functions. Finally, we give conditions for a marginal function to be subregular and semismooth.This research was supported in part by the Fondo Nacional de Ciencias, Santiago, Chile.The authors thank A. Auslender and L. Thibault for discussions on the subject.     

复Clifford分析中的超单演函数

该文研究复Clifford分析中的超单演函数,即方程z_n Df(z)+(n-1)Qf′=0的解. 记f(z)=Pf(z)+Qf(z)e_n,f(z)∈C^2(Ω),f(z): Ω → C^{n+1},Ω C^{n+1}，得出超单演函数的几个性质.     

Generalized B-vex functions and generalized B-vex programming

A class of functions called pseudo B-vex and quasi B-vex functions is introduced by relaxing the definitions of B-vex, pseudoconvex, and quasiconvex functions. Similarly, the class of B-invex, pseudo B-invex, and quasi B-invex functions is defined as a generalization of B-vex, pseudo B-vex, and quasi B-vex functions. The sufficient optimality conditions and duality results are obtained for a nonlinear programming problem involving B-vex and B-invex functions.The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319. The second author is grateful to the Faculty of Management, University of Manitoba for the financial support provided for her visit. The authors are thankful to Prof. R. N. Kaul, Department of Mathematics, Delhi University for his constructive criticism of the paper.     

积分算子作用下的亚纯多叶函数

令∑_p表示形如f(z)=z~(-p)+∑m=1∞(p∈N={1,2,3…})且在去心单位开圆盘D=U\{0}={z∶z∈C且0|z|1}上解析的亚纯多叶函数类.利用一个作用在∑_p上的乘积算子定义了几个新的亚纯函数的子类,并考虑这些函数类在积分算子作用下的性质.     

Directional derivatives of optimal value functions in mathematical programming

This note discusses the existence of the directional derivatives of the optimal value functions in a class of nonlinear programming problems and gives the expressions of the directional derivatives. In the study, it is not assumed that the optimal set at the point discussed is not empty. Many well-known results of this area can be derived as special cases of the main theorems of this note.This research was supported by the National Science Foundation of China. The authors would like to thank Professor A. V. Fiacco and the referees for their helpful suggestions.     

圆对称函数的相邻系数

研究了圆对称函数的Goluzin问题.当f为圆对称函数,λ=k1(k=2,3,…)时,通过构造一个正实部函数,利用积分方法,得到了k次圆对称函数相邻系数模之差的精确估计.另外,还得到了圆对称函数的积分表示.     

3D deformations by means of monogenic functions

In this paper, the authors compute the coefficient of quasiconformality for monogenic functions in an arbitrary ball of the Euclidean space . This quantification may be needed in applications but also appears to be of intrinsic interest. The main tool used is a 3D Fourier series development of monogenic functions in terms of a special set of solid spherical monogenics. Ultimately, we present some examples showing the applicability of our approach. Copyright © 2012 John Wiley & Sons, Ltd.